Question: Simplify; express your answer in exponential form. Assume $q\neq 0, n\neq 0$. $\dfrac{{(q^{-3})^{-5}}}{{(q^{5}n^{-3})^{3}}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${q^{-3}}$ to the exponent ${-5}$ . Now ${-3 \times -5 = 15}$ , so ${(q^{-3})^{-5} = q^{15}}$ In the denominator, we can use the distributive property of exponents. ${(q^{5}n^{-3})^{3} = (q^{5})^{3}(n^{-3})^{3}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(q^{-3})^{-5}}}{{(q^{5}n^{-3})^{3}}} = \dfrac{{q^{15}}}{{q^{15}n^{-9}}}$ Break up the equation by variable and simplify. $\dfrac{{q^{15}}}{{q^{15}n^{-9}}} = \dfrac{{q^{15}}}{{q^{15}}} \cdot \dfrac{{1}}{{n^{-9}}} = q^{{15} - {15}} \cdot n^{- {(-9)}} = n^{9}$.